Abstract

We establish duality for monogamy of entanglement: whereas monogamy of entanglementinequalities provide an upper bound for bipartite sharability of entanglement in a multipartite system, as quantified by linear entropy, we prove that the same quantity (namely, linear entropy) provides a lower bound for distribution of bipartite entanglement in a multipartite system. Our theorem for monogamy of entanglement is used to establish relations between bipartite entanglement that separate one qubit from the rest versus separating two qubits from the rest.

Received 20 June 2006Accepted 08 December 2006Published online 31 January 2007

Acknowledgments:

One of the authors (G.G.) appreciates valuable discussions with David Meyer, Peter Stevenhagen, and Nolan Wallach and acknowledges financial support by the National Science Foundation under Grant No. ECS-0202087. Two of the authors (S.B. and B.C.S.) acknowledge financial support from Alberta’s Informatics Circle of Research Excellence (iCORE), the Canadian Institute for Advanced Research, the Canadian Network of Centres of Excellence for the Mathematics of Information Technology and Complex Systems (MITACS), the Natural Sciences and Engineering Research Council, General Dynamics Canada, and the Australian Research Council.